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Math Help - bottle cup and container problem

  1. #1
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    bottle cup and container problem

    Dear Sir,

    I need some help to know the solution of the below question.

    Thanks
    Kingman



    John used 2/5 of a bottle of water to fill some cups and 5/9 of the remaining water to fill 4 containers.
    The capacity of each container was 5 times that of a cup. How many cups did he fill with water?
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  2. #2
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    Hi kingman,
    What have you tried? Let x = liters in bottle ( any units will do ). Express each operation in terms of x.You can write a simple equation in x. Try it


    bjh
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  3. #3
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    ok lets say u have Y units of water. so (5/9)Y = 4C where C = the capacity of the containers. Now the question tells u that C = 5D (D = capacity of the cups)

    After defining all the terms, this should be a simple substitution problem where if C = 5D then (5/9) = 4 (5D) = 20D
    Therefore (1/9) = 4D (20/5 = 4)
    so 1/9 of the total water you have fills up 4 cups, therefore 2/9 fills up 8 cups

    Thank me for doing your homework ^^
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  4. #4
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    Thanks very much for the help but the answer is 24!
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  5. #5
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    That's because holaboo misunderstood the problem. He is assuming that 5/9 of the whole bottle will fill 4 containers when it is said that 5/9 of the remaining water will fill 4 containers. If you use 2/5 of the bottle to fill the cups then there is 1- 2/5= 3/5 of the bottle remaining. 5/9 of 3/5= 3/9= 1/3 of the water in the bottle. That fills 4 containers which is the same as 20 cups. If 1/3 of the water fills 20 cups, how many cups will 2/5 fill? That's a fairly simple proportion. Set up as an equality of fractions, \frac{20}{\frac{1}{3}}= \frac{x}{\frac{2}{5}}, and solve for x.
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